A Residual Inverse Power Method

The inverse power method involves solving shifted equations of theform $(A -\sigma I)v = u$. This paper describes a variant method in
which shifted equations may be solved to a fixed reduced accuracy
without affecting convergence. The idea is to alter the right-hand
side to produce a correction step to be added to the current
approximations. The digits of this step divide into two parts:
leading digits that correct the solution and trailing garbage. Hence
the step can be be evaluated to a reduced accuracy corresponding to
the correcting digits. The cost is an additional multiplication by
$A$ at each step to generate the right-hand side. Analysis and
experiments show that the method is suitable for normal and mildly
nonnormal problems.